Problem: Rewrite as a simplified fraction. ${0.\overline{7} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 7.7777...\\ 1x &= 0.7777...\end{align*}}$ Subtracting the two equations, we have: ${9x = 7}$ ${x = \dfrac{7}{9}} $